@article{Zhang2010,
author = {Zhang, Hao and El‐Shaarawi, A},
doi = {10.1002/env},
file = {:Users/samorris/Dropbox/Mendeley/Environmetrics/Zhang, El‐Shaarawi - 2010 - On spatial skew‐Gaussian processes and applications.pdf:pdf},
journal = {Environmetrics},
keywords = {em algorithm,ern covariogram,mat,skew-gaussian process,skew-normal distribution,slice},
number = {October 2008},
pages = {33--47},
title = {{On spatial skew‐Gaussian processes and applications}},
url = {http://onlinelibrary.wiley.com/doi/10.1002/env.982/abstract},
year = {2010}
}
@article{Sahu2003,
author = {Sahu, Sujit K. and Dey, Dipak K. and Branco, M\'{a}rcia D.},
doi = {10.2307/3316064},
file = {:Users/samorris/Dropbox/Mendeley/Canadian Journal of Statistics/Sahu, Dey, Branco - 2003 - A new class of multivariate skew distributions with applications to bayesian regression models.pdf:pdf},
issn = {03195724},
journal = {Canadian Journal of Statistics},
keywords = {62105,62h12,andphrases,bayesian inference,elliptical distributions,gibbs sampler,heavy tailed error dis-,markov chain monte carlo,msc 2000,multivariate skewness,primary 62f15,secondary 62e15,tribution},
month = jun,
number = {2},
pages = {129--150},
title = {{A new class of multivariate skew distributions with applications to bayesian regression models}},
url = {http://doi.wiley.com/10.2307/3316064},
volume = {31},
year = {2003}
}
@article{Azzalini1999,
author = {Azzalini, a. and Capitanio, a.},
doi = {10.1111/1467-9868.00194},
file = {:Users/samorris/Dropbox/Mendeley/Journal of the Royal Statistical Society Series B (Statistical Methodology)/Azzalini, Capitanio - 1999 - Statistical applications of the multivariate skew normal distribution.pdf:pdf},
issn = {1369-7412},
journal = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
keywords = {elliptical distributions,multivariate normal distribution,quadratic forms,skew normal distribution,skewness},
month = aug,
number = {3},
pages = {579--602},
title = {{Statistical applications of the multivariate skew normal distribution}},
url = {http://doi.wiley.com/10.1111/1467-9868.00194},
volume = {61},
year = {1999}
}
@article{Branco2001,
author = {Branco, M\'{a}rcia D. and Dey, Dipak K.},
doi = {10.1006/jmva.2000.1960},
file = {:Users/samorris/Dropbox/Mendeley/Journal of Multivariate Analysis/Branco, Dey - 2001 - A General Class of Multivariate Skew-Elliptical Distributions.pdf:pdf},
issn = {0047259X},
journal = {Journal of Multivariate Analysis},
keywords = {and phrases,elliptical distributions,exponential power family,mixture,of normals,pearson type ii,skewness},
month = oct,
number = {1},
pages = {99--113},
title = {{A General Class of Multivariate Skew-Elliptical Distributions}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0047259X00919602},
volume = {79},
year = {2001}
}
@article{Azzalini1996,
author = {Azzalini, A},
doi = {10.1093/biomet/83.4.715},
file = {:Users/samorris/Dropbox/Mendeley/Biometrika/Azzalini - 1996 - The multivariate skew-normal distribution.pdf:pdf},
issn = {0006-3444},
journal = {Biometrika},
month = dec,
number = {4},
pages = {715--726},
title = {{The multivariate skew-normal distribution}},
url = {http://biomet.oxfordjournals.org/content/83/4/715.short http://biomet.oupjournals.org/cgi/doi/10.1093/biomet/83.4.715},
volume = {83},
year = {1996}
}
@book{Gupta2013,
address = {New York, NY},
author = {Gupta, Arjun K. and Varga, Tamas and Bodnar, Taras},
doi = {10.1007/978-1-4614-8154-6},
file = {:Users/samorris/Dropbox/Mendeley/Unknown/Gupta, Varga, Bodnar - 2013 - Elliptically Contoured Models in Statistics and Portfolio Theory.pdf:pdf},
isbn = {978-1-4614-8153-9},
publisher = {Springer New York},
title = {{Elliptically Contoured Models in Statistics and Portfolio Theory}},
url = {http://link.springer.com/10.1007/978-1-4614-8154-6},
year = {2013}
}
@article{Gupta2004,
author = {Gupta, Arjun K. and Gonz\'{a}lez-Farı́as, Graciela and Domı́nguez-Molina, J.Armando},
doi = {10.1016/S0047-259X(03)00131-3},
file = {:Users/samorris/Dropbox/Mendeley/Journal of Multivariate Analysis/Gupta, Gonz\'{a}lez-Farı́as, Domı́nguez-Molina - 2004 - A multivariate skew normal distribution.pdf:pdf},
issn = {0047259X},
journal = {Journal of Multivariate Analysis},
keywords = {conditional,contours,density,generating function,marginal,moment,moments,non-normal models,regression},
month = apr,
number = {1},
pages = {181--190},
title = {{A multivariate skew normal distribution}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0047259X03001313},
volume = {89},
year = {2004}
}
@article{Allard2007,
author = {Allard, Denis and Naveau, Philippe},
doi = {10.1080/03610920601126290},
file = {:Users/samorris/Dropbox/Mendeley/Communications in Statistics - Theory and Methods/Allard, Naveau - 2007 - A New Spatial Skew-Normal Random Field Model.pdf:pdf},
issn = {0361-0926},
journal = {Communications in Statistics - Theory and Methods},
keywords = {multivariate},
month = jul,
number = {9},
pages = {1821--1834},
title = {{A New Spatial Skew-Normal Random Field Model}},
url = {http://www.tandfonline.com/doi/abs/10.1080/03610920601126290},
volume = {36},
year = {2007}
}
@article{Minozzo2012,
author = {Minozzo, Marco and Ferracuti, Laura},
file = {:Users/samorris/Dropbox/Mendeley/Chilean Journal of Statistics (ChJS)/Minozzo, Ferracuti - 2012 - On the existence of some skew-normal stationary processes.pdf:pdf},
journal = {Chilean Journal of Statistics (ChJS)},
keywords = {autocorrelation function,generalized linear mixed model,geostatistics,mathematics subject classification,multivariate skew-normal distribution,primary 62m30,secondary 62h11,spatial process,stationary process},
number = {2},
pages = {157--170},
title = {{On the existence of some skew-normal stationary processes.}},
url = {http://chjs.deuv.cl/Vol3N2/ChJS-03-02-04.pdf},
volume = {3},
year = {2012}
}
@phdthesis{Huser2013,
abstract = {Risk assessment for extreme natural phenomena has become increasingly important, and over the past few years the scientific community has realized the importance of considering the spatial or spatio-temporal extent of extreme events. Historically, the GEV and GPD distributions have played an important role in the statistical modeling of extremes at individual locations, but for risk assessment it is crucial to assess dependence between locations: if dependence is strong, extreme events might occur simultaneously at different locations, thereby increasing the overall risk. In this thesis, we construct new dependence models for space-time extremes, based on asymptotically justified arguments, and propose novel inference methods for fitting these models to observations exceeding high thresholds. So far, the modeling of spatial extremes has been limited to fitting max-stable processes to block (usually annual) maxima, regarded as mutually independent. Our threshold-based approach is more efficient and enables more detailed analysis of extremes, but requires a more sophisticated treatment of dependence. The present work also describes how composite likelihoods can be used for inference, establishes the asymptotic distribution of the corresponding estimators, and assesses statistical efficiency for these methods in various contexts. The methodology is illustrated by application to hourly rainfall data from western Switzerland, and enables realistic modeling of their extremal properties.},
author = {Huser, R.},
doi = {10.5075/epfl-thesis-5946.},
file = {:Users/samorris/Dropbox/Mendeley/Unknown/Huser - 2013 - Statistical Modeling and Inference for Spatio-Temporal Extremes.pdf:pdf},
keywords = {Asymptotic independence,Composite likelihood,Extreme event,Max- stable process,Rainfall data,Relative efficiency,Spatio-temporal dependence,Threshold exceedance},
pages = {291},
title = {{Statistical Modeling and Inference for Spatio-Temporal Extremes}},
url = {http://infoscience.epfl.ch/record/188557/files/EPFL\_TH5946.pdf},
volume = {5946},
year = {2013}
}
@article{Schmidt2002,
author = {Schmidt, Rafael},
doi = {10.1007/s001860200191},
file = {:Users/samorris/Dropbox/Mendeley/Mathematical Methods of Operations Research/Schmidt - 2002 - Tail dependence for elliptically contoured distributions.pdf:pdf},
issn = {1432-2994},
journal = {Mathematical Methods of Operations Research},
keywords = {elliptical distribution,regular variation,spherical distribution,tail dependence},
month = may,
number = {2},
pages = {301--327},
title = {{Tail dependence for elliptically contoured distributions}},
url = {http://link.springer.com/10.1007/s001860200191},
volume = {55},
year = {2002}
}
@article{Clauset2013,
abstract = {Quantities with right-skewed distributions are ubiquitous in complex social systems, including political conflict, economics and social networks, and these systems sometimes produce extremely large events. For instance, the 9/11 terrorist events produced nearly 3000 fatalities, nearly six times more than the next largest event. But, was this enormous loss of life statistically unlikely given modern terrorism's historical record? Accurately estimating the probability of such an event is complicated by the large fluctuations in the empirical distribution's upper tail. We present a generic statistical algorithm for making such estimates, which combines semi-parametric models of tail behavior and a non-parametric bootstrap. Applied to a global database of terrorist events, we estimate the worldwide historical probability of observing at least one 9/11-sized or larger event since 1968 to be 11-35\%. These results are robust to conditioning on global variations in economic development, domestic versus international events, the type of weapon used and a truncated history that stops at 1998. We then use this procedure to make a data-driven statistical forecast of at least one similar event over the next decade.},
archivePrefix = {arXiv},
arxivId = {1209.0089},
author = {Clauset, Aaron and Woodard, Ryan},
eprint = {1209.0089},
file = {:Users/samorris/Dropbox/Mendeley/The Annals of Applied Statistics/Clauset, Woodard - 2013 - Estimating the historical and future probabilities of large terrorist events.pdf:pdf},
journal = {The Annals of Applied Statistics},
month = sep,
pages = {9},
title = {{Estimating the historical and future probabilities of large terrorist events}},
url = {http://arxiv.org/abs/1209.0089},
year = {2013}
}
@article{Reich2013,
author = {Reich, Brian J. and Porter, Michael D.},
file = {:Users/samorris/Dropbox/Mendeley/The Annals of Applied Statistics/Reich, Porter - 2013 - Discussion of clauset and woodard.pdf:pdf},
journal = {The Annals of Applied Statistics},
pages = {1--5},
title = {{Discussion of clauset and woodard}},
year = {2013}
}
@article{EugeniaCastellanos2007,
author = {{Eugenia Castellanos}, M. and Cabras, Stefano},
doi = {10.1016/j.jspi.2006.01.006},
file = {:Users/samorris/Dropbox/Mendeley/Journal of Statistical Planning and Inference/Eugenia Castellanos, Cabras - 2007 - A default Bayesian procedure for the generalized Pareto distribution.pdf:pdf},
issn = {03783758},
journal = {Journal of Statistical Planning and Inference},
keywords = {bayesian inference,extreme value theory,jeffreys,peaks over the threshold,s prior},
month = feb,
number = {2},
pages = {473--483},
title = {{A default Bayesian procedure for the generalized Pareto distribution}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0378375806000395},
volume = {137},
year = {2007}
}
@article{Nascimento2011,
author = {Nascimento, Fernando Ferraz and Gamerman, Dani and Lopes, Hedibert Freitas},
doi = {10.1007/s11222-011-9270-z},
file = {:Users/samorris/Dropbox/Mendeley/Statistics and Computing/Nascimento, Gamerman, Lopes - 2011 - A semiparametric Bayesian approach to extreme value estimation.pdf:pdf},
isbn = {1122201192},
issn = {0960-3174},
journal = {Statistics and Computing},
keywords = {bayesian,gpd,higher quantiles,mcmc,nonparametric estimation of curves,threshold estimation},
month = aug,
number = {2},
pages = {661--675},
title = {{A semiparametric Bayesian approach to extreme value estimation}},
url = {http://link.springer.com/10.1007/s11222-011-9270-z},
volume = {22},
year = {2011}
}
@article{Wadsworth2013,
author = {Wadsworth, Jennifer L. and Tawn, Jonathan A.},
file = {:Users/samorris/Dropbox/Mendeley/Biometrika/Wadsworth, Tawn - 2013 - Efficient inference for spatial extreme value processes associated to log-Gaussian random functions.pdf:pdf},
journal = {Biometrika},
keywords = {Extreme value theory,Likelihood inference,Max-stable process,Poisson process,Spatial extremes},
pages = {1 -- 15},
title = {{Efficient inference for spatial extreme value processes associated to log-Gaussian random functions}},
year = {2013}
}
@article{Huser2014,
abstract = {Max-stable processes are the natural analogues of the generalized extreme-value distribution for the modelling of extreme events in space and time. Under suitable conditions, these processes are asymptotically justified models for maxima of independent replications of random fields, and they are also suitable for the modelling of joint individual extreme measurements over high thresholds. This paper extends a model of Schlather (2001) to the space-time framework, and shows how a pairwise censored likelihood can be used for consistent estimation under mild mixing conditions. Estimator efficiency is also assessed and the choice of pairs to be included in the pairwise likelihood is discussed based on computations for simple time series models. The ideas are illustrated by an application to hourly precipitation data over Switzerland.},
archivePrefix = {arXiv},
arxivId = {1201.3245},
author = {Huser, R. and Davison, A. C.},
doi = {10.1111/rssb.12035},
eprint = {1201.3245},
file = {:Users/samorris/Dropbox/Mendeley/Journal of the Royal Statistical Society Series B (Statistical Methodology)/Huser, Davison - 2014 - Space-time modelling of extreme events.pdf:pdf},
issn = {13697412},
journal = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
keywords = {composite likelihood,dom set,extremal coefficient,max-stable process,rainfall data,ran-,threshold-based inference},
month = mar,
number = {2},
pages = {439--461},
title = {{Space-time modelling of extreme events}},
url = {http://arxiv.org/abs/1201.3245 http://doi.wiley.com/10.1111/rssb.12035},
volume = {76},
year = {2014}
}
@article{Davison2013,
author = {Davison, A. C. and Huser, R. and Thibaud, E.},
doi = {10.1007/s11004-013-9469-y},
file = {:Users/samorris/Dropbox/Mendeley/Mathematical Geosciences/Davison, Huser, Thibaud - 2013 - Geostatistics of Dependent and Asymptotically Independent Extremes.pdf:pdf},
issn = {1874-8961},
journal = {Mathematical Geosciences},
keywords = {asymptotic independence,brown,gaussian process,generalised pareto distribution,max-stable process,resnick process,statistics of extremes},
month = jun,
number = {5},
pages = {511--529},
title = {{Geostatistics of Dependent and Asymptotically Independent Extremes}},
url = {http://link.springer.com/10.1007/s11004-013-9469-y},
volume = {45},
year = {2013}
}
@article{Gelfand2005,
abstract = {Customary modeling for continuous point-referenced data assumes a Gaussian process that is often taken to be stationary. When such models are fitted within a Bayesian framework, the unknown parameters of the process are assumed to be random, so a random Gaussian process results. Here we propose a novel spatial Dirichlet process mixture model to produce a random spatial process that is neither Gaussian nor stationary. We first develop a spatial Dirichlet process model for spatial data and discuss its properties. Because of familiar limitations associated with direct use of Dirichlet process models, we introduce mixing by convolving this process with a pure error process. We then examine properties of models created through such Dirichlet process mixing. In the Bayesian framework, we implement posterior inference using Gibbs sampling. Spatial prediction raises interesting questions, but these can be handled. Finally, we illustrate the approach using simulated data, as well as a dataset involving precipitation measurements over the Languedoc-Roussillon region in southern France.},
author = {Gelfand, Alan E. and Kottas, Athanasios and MacEachern, Steven N.},
doi = {10.1198/016214504000002078},
file = {:Users/samorris/Dropbox/Mendeley/Journal of the American Statistical Association/Gelfand, Kottas, MacEachern - 2005 - Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing.pdf:pdf},
issn = {0162-1459},
journal = {Journal of the American Statistical Association},
keywords = {dependent dirichlet process,dirichlet process mixture models,gaussian process,markov chain monte carlo,nonsta-,point-referenced spatial data,random distribution,tionarity},
month = sep,
number = {471},
pages = {1021--1035},
title = {{Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing}},
url = {http://www.tandfonline.com/doi/abs/10.1198/016214504000002078},
volume = {100},
year = {2005}
}
@article{Fuentes2012,
abstract = {Estimating the probability of extreme temperature events is difficult because of limited records across time and the need to extrapolate the distributions of these events, as opposed to just the mean, to locations where observations are not available. Another related issue is the need to characterize the uncertainty in the estimated probability of extreme events at different locations. Although the tools for statistical modeling of univariate extremes are well-developed, extending these tools to model spatial extreme data is an active area of research. In this paper, in order to make inference about spatial extreme events, we introduce a new nonparametric model for extremes. We present a Dirichlet-based copula model that is a flexible alternative to parametric copula models such as the normal and t-copula. The proposed modelling approach is fitted using a Bayesian framework that allow us to take into account different sources of uncertainty in the data and models. We apply our methods to annual maximum temperature values in the east-south-central United States.},
author = {Fuentes, Montserrat and Henry, John and Reich, Brian},
doi = {10.1007/s10687-012-0154-1},
file = {:Users/samorris/Dropbox/Mendeley/Extremes/Fuentes, Henry, Reich - 2012 - Nonparametric spatial models for extremes application to extreme temperature data.pdf:pdf},
issn = {1386-1999},
journal = {Extremes},
keywords = {dirichlet processes,extreme temperatures,nonstationarity,return levels,spatial models},
month = aug,
number = {1},
pages = {75--101},
title = {{Nonparametric spatial models for extremes: application to extreme temperature data}},
url = {http://link.springer.com/10.1007/s10687-012-0154-1},
volume = {16},
year = {2012}
}
@article{Coles1991,
abstract = {The classical treatment of multivariate extreme values is through componentwise ordering, though in practice most interest is in actual extreme events. Here the point process of observations which are extreme in at least one component is considered. Parametric models for the dependence between components must satisfy certain constraints. Two new techniques for generating such models are presented. Aspects of the statistical estimation of the resulting models are discussed and are illustrated with an application to oceanographic data.},
author = {Coles, Stuart G. and Tawn, Jonathan A.},
file = {:Users/samorris/Dropbox/Mendeley/Journal of the Royal Statistical Society Series B (Methodological)/Coles, Tawn - 1991 - Modelling Extreme Multivariate Events.pdf:pdf},
journal = {Journal of the Royal Statistical Society: Series B (Methodological)},
keywords = {extreme value theory,generalized pareto distribution,likelihood,maximum,multivariate ordering,non-homogeneous poisson process},
number = {2},
pages = {377--392},
title = {{Modelling Extreme Multivariate Events}},
url = {http://www.jstor.org/stable/10.2307/2345748},
volume = {53},
year = {1991}
}
@phdthesis{Tajvidi1996,
author = {Tajvidi, Nader},
file = {:Users/samorris/Dropbox/Mendeley/Unknown/Tajvidi - 1996 - Characterisation and Some Statistical Aspects of Univariate and Multivariate Generalised Pareto Distributions.pdf:pdf},
isbn = {91-7197-390-7},
school = {G\"{o}teborg},
title = {{Characterisation and Some Statistical Aspects of Univariate and Multivariate Generalised Pareto Distributions}},
year = {1996}
}
@article{Wang2010,
abstract = {In the information system research, a question of particular interest is to interpret and to predict the probability of a firm to adopt a new technology such that market promotions are targeted to only those firms that were more likely to adopt the technology. Typically, there exists significant difference between the observed number of “adopters” and “nonadopters,” which is usually coded as binary response. A critical issue involved in modeling such binary response data is the appropriate choice of link functions in a regression model. In this paper we introduce a new flexible skewed link function for modeling binary response data based on the generalized extreme value (GEV) distribution. We show how the proposed GEV links provide more flexible and improved skewed link regression models than the existing skewed links, especially when dealing with imbalance between the observed number of 0’s and 1’s in a data. The flexibility of the proposed model is illustrated through simulated data sets and a billing data set of the electronic payments system adoption from a Fortune 100 company in 2005.},
author = {Wang, Xia and Dey, Dipak K.},
doi = {10.1214/10-AOAS354},
file = {:Users/samorris/Dropbox/Mendeley/The Annals of Applied Statistics/Wang, Dey - 2010 - Generalized extreme value regression for binary response data An application to B2B electronic payments system adopti.pdf:pdf},
issn = {1932-6157},
journal = {The Annals of Applied Statistics},
keywords = {generalized extreme value distribution,latent variable,markov chain monte carlo,posterior distribution,skewness},
month = dec,
number = {4},
pages = {2000--2023},
title = {{Generalized extreme value regression for binary response data: An application to B2B electronic payments system adoption}},
url = {http://projecteuclid.org/euclid.aoas/1294167807},
volume = {4},
year = {2010}
}
@article{Tawn1990,
abstract = {Multivariate extreme value distributions arise as the limiting joint distribution of normalized componentwise maxima/minima. No parametric family exists for the dependence between the margins. This paper extends to more than two variables the models and results for the bivariate case obtained by Tawn (1988). Two new families of physically motivated parametric models for the dependence structure are presented and are illustrated with an application to trivariate extreme sea level data.},
author = {Tawn, Jonathan A.},
doi = {10.1093/biomet/77.2.245},
file = {:Users/samorris/Dropbox/Mendeley/Biometrika/Tawn - 1990 - Modelling multivariate extreme value distributions.pdf:pdf},
issn = {0006-3444},
journal = {Biometrika},
keywords = {Extreme value theory,Generalized Pareto distribution,Multivariate exponential distribution,Nonregular estimation},
number = {2},
pages = {245--253},
title = {{Modelling multivariate extreme value distributions}},
url = {http://biomet.oxfordjournals.org/cgi/doi/10.1093/biomet/77.2.245},
volume = {77},
year = {1990}
}
@misc{Smith1990,
abstract = {Max-stable processes arise from an infinite-dimensional generalisation of extreme value theory. They form a natural class of processes when sample maxima are observed at each site of a spatial process, a problem of particular interest in connection with regional estimation methods in hydrology. A general representation of max-stable processes due to de Haan and Vatan is discussed, and examples are given to show how it may be used to generate explicit examples of max-stable process. As a side-product, it is possible to generate a number of known multivariate extreme value families in this way, and in one case this suggests an extension of the family. The main contribution of the paper, however, is to define two new max-stable stochastic processes, related to the multivariate normal and multivariate t distributions. Statistical estimation and model checking are discussed, and the concepts illustrated by being applied to rainfall data. Keywords.},
author = {Smith, Richard L.},
file = {:Users/samorris/Dropbox/Mendeley/Unknown/Smith - 1990 - Max-stable processes and spatial extremes.pdf:pdf},
keywords = {Gaussian extreme value process,hydrological extremes,max-stable process,multivariate extreme value theory},
title = {{Max-stable processes and spatial extremes}},
year = {1990}
}
@article{Stephenson2003,
abstract = {Methods are given for simulating from symmetric and asymmetric versions of the multivariate logistic distribution, and from other multivariate extreme value distributions based on the well known logistic model. We consider two general approaches. The first approach uses transformations to derive random variables with a joint distribution function from which it is easy to simulate. The second approach derives from a specification of conditionally independent marginal components, conditioning on positive stable random variables. This specification extends to models of nested or hierarchical type and leads to an efficient way of incorporating marginal censoring. The algorithms presented in Sections 2 and 3 are available on request from the author. They are also included in the R (Ihaka and Gentleman, 1996) package evd (Stephenson, 2002), which is available from http://www.maths.lancs.ac.uk/\~{}stephena/.},
author = {Stephenson, Alec},
doi = {10.1023/A:1026277229992},
file = {:Users/samorris/Dropbox/Mendeley/Extremes/Stephenson - 2003 - Simulating Multivariate Extreme Value Distributions of Logistic Type.pdf:pdf},
journal = {Extremes},
keywords = {multivariate extreme value distribution,positive stable distribution,simulation},
number = {1},
pages = {49--59},
title = {{Simulating Multivariate Extreme Value Distributions of Logistic Type}},
url = {http://link.springer.com/article/10.1023/A:1026277229992},
volume = {6},
year = {2003}
}
@article{Stephenson2009,
abstract = {Multivariate extreme events are typically modelled using multivariate extreme value distributions. Unfortunately, there exists no finite parametrization for the class of multivariate extreme value distributions. One common approach is to model extreme events using some flexible parametric subclass. This approach has been limited to only two or three dimensions, primarily because suitably flexible high-dimensional parametric models have prohibitively complex density functions. We present an approach that allows a number of popular flexible models to be used in arbitrarily high dimensions. The approach easily handles missing and censored data, and can be employed when modelling componentwise maxima and multivariate threshold exceedances. The approach is based on a representation using conditionally independent marginal components, conditioning on positive stable random variables. We use Bayesian inference, where the conditioning variables are treated as auxiliary variables within Markov chain Monte Carlo simulations. We demonstrate these methods with an application to sea-levels, using data collected at 10 sites on the east coast of England.},
author = {Stephenson, Alec G.},
doi = {10.1111/j.1467-842X.2008.00528.x},
file = {:Users/samorris/Dropbox/Mendeley/Australian \& New Zealand Journal of Statistics/Stephenson - 2009 - High-Dimensional Parametric Modelling of Multivariate Extreme Events.pdf:pdf},
issn = {13691473},
journal = {Australian \& New Zealand Journal of Statistics},
keywords = {markov chain monte carlo,maxima,multivariate extreme value distribution,positive stable distribution,sea-level},
month = mar,
number = {1},
pages = {77--88},
title = {{High-Dimensional Parametric Modelling of Multivariate Extreme Events}},
url = {http://doi.wiley.com/10.1111/j.1467-842X.2008.00528.x},
volume = {51},
year = {2009}
}
@article{Silva2008,
abstract = {Copula functions and marginal distributions are combined to produce multivariate distributions. We show advantages of estimating all parameters of these models using the Bayesian approach, which can be done with standard Markov chain Monte Carlo algorithms. Deviance-based model selection criteria are also discussed when applied to copula models since they are invariant under monotone increasing transformations of the marginals. We focus on the deviance information criterion. The joint estimation takes into account all dependence structure of the parameters’ posterior distributions in our chosen model selection criteria. Two Monte Carlo studies are conducted to show that model identification improves when the model parameters are jointly estimated. We study the Bayesian estimation of all unknown quantities at once considering bivariate copula functions and three known marginal distributions.},
author = {Silva, Ralph Dos Santos and Lopes, Hedibert Freitas},
doi = {10.1007/s11222-008-9058-y},
file = {:Users/samorris/Dropbox/Mendeley/Statistics and Computing/Silva, Lopes - 2008 - Copula, marginal distributions and model selection a Bayesian note.pdf:pdf},
issn = {0960-3174},
journal = {Statistics and Computing},
keywords = {Monte Carlo study,copula,deviance information criterion,marginal distribution,measure of dependence,skewness},
month = mar,
number = {3},
pages = {313--320},
title = {{Copula, marginal distributions and model selection: a Bayesian note}},
url = {http://link.springer.com/10.1007/s11222-008-9058-y},
volume = {18},
year = {2008}
}
@article{Schlather2002,
abstract = {Models for stationary max-stable random fields are revisited and illustrated by two-dimensional simulations. We introduce a new class of models, which are based on stationary Gaussian random fields, and whose realizations are not necessarily semi-continuous functions. The bivariate marginal distributions of these random fields can be calculated, and they form a new class of bivariate extreme value distributions.},
author = {Schlather, Martin},
doi = {10.1023/A:1020977924878},
file = {:Users/samorris/Dropbox/Mendeley/Extremes/Schlather - 2002 - Models for Stationary Max-Stable Random Fields.pdf:pdf},
journal = {Extremes},
keywords = {Gaussian random field,bivariate extreme value distribution,dependence function,max-stable random field,rainfall modeling,simulation of max-stable processes},
number = {1},
pages = {33--44},
title = {{Models for Stationary Max-Stable Random Fields}},
url = {http://link.springer.com/article/10.1023/A:1020977924878},
volume = {5},
year = {2002}
}
@phdthesis{Sang2008,
abstract = {Extreme value theory finds wide applications in areas such as environmental science, financial strategy of risk management and biomedical data processing. In this thesis, we present two spatial extreme value studies related to weather and climate events observed in space and in time, one of which motivates a novel methodology in constructing continuous spatial process for extreme values. Motivated by finding multiscale spatial dependence in extreme climate studies, we offer a new Bayesian analysis tool for learning about both large scale spatial dependence and microscale dependence. The last chapter presents a novel application of space-time models to synoptic climatology. The first investigation is a development of hierarchical modeling approach for explaining a collection of spatially-referenced time series of extreme values. We assume that the observations follow Generalized Extreme Value(GEV) distributions whose locations and scales are jointly spatially dependent where the dependence is captured using multivariate Markov random field models specified through coregionalization. There are various ways to provide appropriate specifications; we consider four choices. The models can be fitted using a Markov Chain Monte Carlo (MCMC) algorithm to enable inference for parameters and to provide spatio-temporal predictions. We fit the models to a set of gridded interpolated precipitation data collected over a 50 year period for the Cape Floristic Region in South Africa, summarizing results for what appears to be the best choice of model. In chapter 3, we extend the hierarchical modeling approach for explaining a collection of point-referenced time series of extreme values. Annual maxima are still assumed to follow GEV distributions, with parameters $\mu$, $\sigma$, and $\xi$ specified in the latent stage to reflect underlying spatio-temporal structure. Here, we relax the conditionally independence assumption previously imposed in the first stage hierarchical models for annual maxima. Instead, a continuous spatial process model is proposed to account for spatial dependence which is unexplained by the latent spatio-temporal specifications for the GEV parameters. In addition, we offer an approach to make spatial interpolation for extreme values based on this hierarchical models with smoothed residuals across space. A simulation study is illustrated to investigate the model fitting behavior. Motivated by the findings in extreme climate studies, which is, large scale spatial variations and small scale spatial variations coexist in some extreme climate phenomena, we present a Bayesian spatial modeling approach to make inference of both large scale and small scale spatial dependence in a general spatial setting. In particular, we focus on the investigation of microscale spatial dependence, which is defined as the dependence at distances smaller than the measurement scale of the spatial study. Since microscale spatial variation study often involves data observed at high resolution, we offer several potential solutions to tackle the computational difficulty of 'large n' problem. In the last chapter, the application we focus on is to synoptic climatology where the goal is to develop an array of atmospheric states to capture a collection of distinct circulations. In particular, Self Organizing Maps (SOMs) are one of the recently used techniques in the meteorology community with regard to developing synoptic weather states. Little discussion about this technique has been found in the statistics literature. We introduce the stochasticity in the form of a space-time process model aiming to illuminate and interpret its performance in the context of application to daily data collection. That is, the observed daily state vectors are viewed as a time series of multivariate process realizations which we try to understand under the dimension reduction achieved by the SOM procedure.},
author = {Sang, Huiyan},
file = {:Users/samorris/Dropbox/Mendeley/Unknown/Sang - 2008 - Extreme value modeling for space-time data with meterological applications.pdf:pdf},
isbn = {9780549965022},
school = {Duke University},
title = {{Extreme value modeling for space-time data with meterological applications}},
url = {http://search.proquest.com.prox.lib.ncsu.edu/docview/304636216?accountid=12725},
year = {2008}
}
@article{Sang2008a,
abstract = {We propose a hierarchical modeling approach for explaining a collection of spatially referenced time series of extreme values. We assume that the observations follow generalized extreme value (GEV) distributions whose locations and scales are jointly spatially dependent where the dependence is captured using multivariate Markov random field models specified through coregionalization. In addition, there is temporal dependence in the locations. There are various ways to provide appropriate specifications; we consider four choices. The models can be fitted using a Markov Chain Monte Carlo (MCMC) algorithm to enable inference for parameters and to provide spatio–temporal predictions. We fit the models to a set of gridded interpolated precipitation data collected over a 50-year period for the Cape Floristic Region in South Africa, summarizing results for what appears to be the best choice of model.},
author = {Sang, Huiyan and Gelfand, Alan E.},
doi = {10.1007/s10651-007-0078-0},
file = {:Users/samorris/Dropbox/Mendeley/Environmental and Ecological Statistics/Sang, Gelfand - 2008 - Hierarchical modeling for extreme values observed over space and time.pdf:pdf},
issn = {1352-8505},
journal = {Environmental and Ecological Statistics},
keywords = {coregionalization,generalized extreme value distribution,markov,precipitation surfaces,random field,spatial random effects},
month = jan,
number = {3},
pages = {407--426},
title = {{Hierarchical modeling for extreme values observed over space and time}},
url = {http://link.springer.com/10.1007/s10651-007-0078-0},
volume = {16},
year = {2008}
}
@article{Rootzen2006,
abstract = {Statistical inference for extremes has been a subject of intensive research over the past couple of decades. One approach is based on modelling exceedances of a random variable over a high threshold with the generalized Pareto (GP) distribution. This has proved to be an important way to apply extreme value theory in practice and is widely used. We introduce a multivariate analogue of the GP distribution and show that it is characterized by each of following two properties: first, exceedances asymptotically have a multivariate GP distribution if and only if maxima asymptotically are extreme value distributed; and second, the multivariate GP distribution is the only one which is preserved under change of exceedance levels. We also discuss a bivariate example and lower-dimensional marginal distributions.},
author = {Rootz\'{e}n, Holger and Tajvidi, Nader},
doi = {10.3150/bj/1161614952},
file = {:Users/samorris/Dropbox/Mendeley/Bernoulli/Rootz\'{e}n, Tajvidi - 2006 - Multivariate generalized Pareto distributions.pdf:pdf},
issn = {1350-7265},
journal = {Bernoulli},
month = oct,
number = {5},
pages = {917--930},
title = {{Multivariate generalized Pareto distributions}},
url = {http://projecteuclid.org/euclid.bj/1161614952},
volume = {12},
year = {2006}
}
@article{Reich2007,
abstract = {Storm surge, the onshore rush of sea water caused by the high winds and low pressure associated with a hurricane, can compound the effects of inland flooding caused by rainfall, leading to loss of property and loss of life for residents of coastal areas. Numerical ocean models are essential for creating storm surge forecasts for coastal areas. These models are driven primarily by the surface wind forcings. Currently, the gridded wind fields used by ocean models are specified by deterministic formulas that are based on the central pressure and location of the storm center. While these equations incorporate important physical knowledge about the structure of hurricane surface wind fields, they cannot always capture the asymmetric and dynamic nature of a hurricane. A new Bayesian multivariate spatial statistical modeling framework is introduced combining data with physical knowledge about the wind fields to improve the estimation of the wind vectors. Many spatial models assume the data follow a Gaussian distribution. However, this may be overly-restrictive for wind fields data which often display erratic behavior, such as sudden changes in time or space. In this paper we develop a semiparametric multivariate spatial model for these data. Our model builds on the stick-breaking prior, which is frequently used in Bayesian modeling to capture uncertainty in the parametric form of an outcome. The stick-breaking prior is extended to the spatial setting by assigning each location a different, unknown distribution, and smoothing the distributions in space with a series of kernel functions. This semiparametric spatial model is shown to improve prediction compared to usual Bayesian Kriging methods for the wind field of Hurricane Ivan.},
author = {Reich, Brian J. and Fuentes, Montserrat},
doi = {10.1214/07-AOAS108},
file = {:Users/samorris/Dropbox/Mendeley/The Annals of Applied Statistics/Reich, Fuentes - 2007 - A multivariate semiparametric Bayesian spatial modeling framework for hurricane surface wind fields.pdf:pdf},
issn = {1932-6157},
journal = {The Annals of Applied Statistics},
keywords = {Hierarchical Bayesian model,Multivariate data,Spatial statistics,Stick-breaking prior,Wind fields},
month = jun,
number = {1},
pages = {249--264},
title = {{A multivariate semiparametric Bayesian spatial modeling framework for hurricane surface wind fields}},
url = {http://projecteuclid.org/euclid.aoas/1183143738},
volume = {1},
year = {2007}
}
@article{Reich2012,
abstract = {Extreme environmental phenomena such as major precipitation events manifestly exhibit spatial dependence. Max-stable processes are a class of asymptotically-justified models that are capable of representing spatial dependence among extreme values. While these models satisfy modeling requirements, they are limited in their utility because their corresponding joint likelihoods are unknown for more than a trivial number of spatial locations, preventing, in particular, Bayesian analyses. In this paper, we propose a new random effects model to account for spatial dependence. We show that our specification of the random effect distribution leads to a max-stable process that has the popular Gaussian extreme value process (GEVP) as a limiting case. The proposed model is used to analyze the yearly maximum precipitation from a regional climate model.},
author = {Reich, Brian J. and Shaby, Benjamin A.},
doi = {10.1214/12-AOAS591},
file = {:Users/samorris/Dropbox/Mendeley/The Annals of Applied Statistics/Reich, Shaby - 2012 - A hierarchical max-stable spatial model for extreme precipitation.pdf:pdf},
issn = {1932-6157},
journal = {The Annals of Applied Statistics},
keywords = {Regional climate model,gaussian extreme value process,generalized extreme value distribution,positive stable distribution},
month = dec,
number = {4},
pages = {1430--1451},
title = {{A hierarchical max-stable spatial model for extreme precipitation}},
url = {http://projecteuclid.org/euclid.aoas/1356629046},
volume = {6},
year = {2012}
}
@article{Reich2013a,
abstract = {Tropospheric ozone is one of six criteria pollutants regulated by the US EPA, and has been linked to respiratory and cardiovascular endpoints and adverse effects on vegetation and ecosystems. Regional photochemical models have been developed to study the impacts of emission reductions on ozone levels. The standard approach is to run the deterministic model under new emission levels and attribute the change in ozone concentration to the emission control strategy. However, running the deterministic model requires substantial computing time, and this approach does not provide a measure of uncertainty for the change in ozone levels. Recently, a reduced form model (RFM) has been proposed to approximate the complex model as a simple function of a few relevant inputs. In this paper, we develop a new statistical approach to make full use of the RFM to study the effects of various control strategies on the probability and magnitude of extreme ozone events. We fuse the model output with monitoring data to calibrate the RFM by modeling the conditional distribution of monitoring data given the RFM using a combination of flexible semiparametric quantile regression for the center of the distribution where data are abundant and a parametric extreme value distribution for the tail where data are sparse. Selected parameters in the conditional distribution are allowed to vary by the RFM value and the spatial location. Also, due to the simplicity of the RFM, we are able to embed the RFM in our Bayesian hierarchical framework to obtain a full posterior for the model input parameters, and propagate this uncertainty to the estimation of the effects of the control strategies. We use the new framework to evaluate three potential control strategies, and find that reducing mobile-source emissions has a larger impact than reducing point-source emissions or a combination of several emission sources.},
author = {Reich, Brian and Cooley, Daniel and Foley, Kristen and Napelenok, Sergey and Shaby, Benjamin},
doi = {10.1214/13-AOAS628},
file = {:Users/samorris/Dropbox/Mendeley/The Annals of Applied Statistics/Reich et al. - 2013 - Extreme value analysis for evaluating ozone control strategies.pdf:pdf},
issn = {1932-6157},
journal = {The Annals of Applied Statistics},
keywords = {Bayesian hierarchical modeling,Generalized Pareto distribution,Spatial data analysis,Statistical downscaling},
month = jun,
number = {2},
pages = {739--762},
title = {{Extreme value analysis for evaluating ozone control strategies}},
url = {http://projecteuclid.org/euclid.aoas/1372338466},
volume = {7},
year = {2013}
}
@article{Morrison1972,
abstract = {There are many types of diverse models that yield probabilistic predictions for outcomes that are binary. We show that a correlation between the 0, 1 binary outcomes and the prediction probabilities can yield meaningful results. The upper bound for the resulting R2 turns out to be a surprisingly simple expression for a class of situations which contain a quite general assumption on the distribution of the prediction probabilities. Some implications for subjective probability estimates are also given.},
author = {Morrison, Donald G.},
doi = {10.1080/01621459.1972.10481207},
file = {:Users/samorris/Dropbox/Mendeley/Journal of the American Statistical Association/Morrison - 1972 - Upper Bounds for Correlations between Binary Outcomes and Probabilistic Predictions.pdf:pdf},
issn = {0162-1459},
journal = {Journal of the American Statistical Association},
month = mar,
number = {337},
pages = {68--70},
title = {{Upper Bounds for Correlations between Binary Outcomes and Probabilistic Predictions}},
url = {http://www.tandfonline.com/doi/abs/10.1080/01621459.1972.10481207},
volume = {67},
year = {1972}
}
@article{Michel2008,
abstract = {The investigation of multivariate generalized Pareto distributions (GPDs) has begun only recently and there are slightly varying definitions of GPDs available. In this article we investigate the one from Section 5.1 of Falk et al. [Laws of Small Numbers: Extremes and Rare Events, second ed., Birkh\"{a}user, Basel, 2004], which does not differ in the area of interest from those of other authors. We first give an interpretation of the case of independence in terms of the peaks-over-threshold approach. This case is also used in dimension d=3 by Falk et al. [Laws of Small Numbers: Extremes and Rare Events, second ed., Birkh\"{a}user, Basel, 2004] as a counterexample to show that GP functions are not necessarily distribution functions on their entire support. We generalize this counterexample to an arbitrary dimension d≥3 and demonstrate also that other GP functions show this behavior. Finally we show that different GPDs can lead to the same conditional probability measure in the area of interest.},
author = {Michel, Ren\'{e}},
doi = {10.1016/j.jmva.2007.08.007},
file = {:Users/samorris/Dropbox/Mendeley/Journal of Multivariate Analysis/Michel - 2008 - Some notes on multivariate generalized Pareto distributions.pdf:pdf},
issn = {0047259X},
journal = {Journal of Multivariate Analysis},
keywords = {angular measure,extreme value distribution,generalized pareto distribution,logistic,peaks over threshold},
month = jul,
number = {6},
pages = {1288--1301},
title = {{Some notes on multivariate generalized Pareto distributions}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0047259X07001169},
volume = {99},
year = {2008}
}
@article{Michel2007,
abstract = {The investigation of multivariate generalized Pareto distributions (GPDs) has begun only recently. For further progress with these distributions simulation methods are an important part. We describe several methods of simulating GPDs, beginning with an efficient method for the logistic GPD. The algorithm is based on the Shi transformation, which was already used for the simulation of multivariate extreme value distributions (EVDs) of logistic type. In the sequel another algorithm is presented simulating a broader class of GPDs. Due to its numerical complexity it is only practicably applicable in low dimensions. A method is given to generate unconditional GPD random vectors from conditionally GPD distributed random vectors. A short application of the simulation methods in the analysis of a real hydrological data set concludes the article. The simulation algorithms are available on the author’s home page http://statistik.mathematik.uni-wuerzburg.de/\~{}michel.},
author = {Michel, Ren\'{e}},
doi = {10.1007/s10687-007-0036-0},
file = {:Users/samorris/Dropbox/Mendeley/Extremes/Michel - 2007 - Simulation of certain multivariate generalized Pareto distributions.pdf:pdf},
isbn = {1068700700360},
issn = {1386-1999},
journal = {Extremes},
keywords = {60g70,62g32,ams 2000 subject classification,generalized pareto distribution,logistic gpd,peaks over threshold,pickands coordinates,primary,rejection method,secondary,shi transformation,simulation},
month = oct,
number = {3},
pages = {83--107},
title = {{Simulation of certain multivariate generalized Pareto distributions}},
url = {http://link.springer.com/10.1007/s10687-007-0036-0},
volume = {10},
year = {2007}
}
@phdthesis{Michel2006,
abstract = {The investigation of multivariate generalized Pareto distributions (GPDs) in the framework of extreme value theory has begun only lately. Recent results show that they can, as in the univariate case, be used in Peaks over Threshold approaches. In this manuscript we investigate the definition of GPDs from Section 5.1 of Falk et al. (2004), which does not differ in the area of interest from those of other authors. We first show some theoretical properties and introduce important examples of GPDs. For the further investigation of these distributions simulation methods are an important part. We describe several methods of simulating GPDs, beginning with an efficient method for the logistic GPD. This algorithm is based on the Shi transformation, which was introduced by Shi (1995) and was used in Stephenson (2003) for the simulation of multivariate extreme value distributions of logistic type. We also present nonparametric and parametric estimation methods in GPD models. We estimate the angular density nonparametrically in arbitrary dimension, where the bivariate case turns out to be a special case. The asymptotic normality of the corresponding estimators is shown. Also in the parametric estimations, which are mainly based on maximum likelihood methods, the asymptotic normality of the estimators is shown under certain regularity conditions. Finally the methods are applied to a real hydrological data set containing water discharges of the rivers Altm\"{u}hl and Danube in southern Bavaria.},
author = {Michel, Ren\'{e}},
file = {:Users/samorris/Dropbox/Mendeley/Unknown/Michel - 2006 - Simulation and estimation in multivariate generalized Pareto models.pdf:pdf},
keywords = {angular density,extreme value theory,multivariate generalized Pareto distributions,peaks over threshold,simulation},
school = {Universit\"{a}t W\"{u}rtzburg},
title = {{Simulation and estimation in multivariate generalized Pareto models}},
url = {http://www.opus-bayern.de/uni-wuerzburg/volltexte/2006/1848/},
year = {2006}
}
@phdthesis{Jeon2012a,
abstract = {The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations. Multivariate extreme value theory can be used to model the joint extremal behavior of environmental data such as precipitation, snow depths or daily temperatures. Max-stable processes are the natural generalization of extremal dependence structures to infinite dimensions arising from the extension of multivariate extreme value theory. However, there have been few works on the threshold approach of max-stable processes. Padoan, Ribatet and Sisson [2010] proposed the maximum composite likelihood approach for fitting max-stable processes to avoid the complexity and unavailability of the multivariate density function. We propose the threshold version of max-stable process estimation and we apply the pairwise composite likelihood method to it. We assume a strict form of condition, so called the second-order regular variation condition, for the distribution satisfying the domain of attraction. To obtain the limit behavior, we also consider the increasing domain structure with stochastic sampling design based on the setting and conditions in Lahiri [2003] and we then establish consistency and asymptotic normality of the estimator for dependence parameter in the threshold method of max-stable processes. The method is studied by simulation and illustrated by the application of temperature data in North Carolina, United States.},
author = {Jeon, Soyoung},
file = {:Users/samorris/Dropbox/Mendeley/Unknown/Jeon - 2012 - Max-stable Processes for Threshold Exceedances.pdf:pdf},
isbn = {9781267420602},
school = {The University of North Carolina at Chapel Hill},
title = {{Max-stable Processes for Threshold Exceedances}},
url = {http://search.proquest.com.prox.lib.ncsu.edu/docview/1026934978?accountid=12725},
year = {2012}
}
@article{Kanter1975,
abstract = {In this paper it is shown that if q is the density of a symmetric stable density, then for c∈(0,1)∪(1,∞), the graph of q(x) intersects the graph of cq(cx) at only two points. The argument proceeds by introducing a new characterization of unimodality for densities and involves a representation for symmetric stable random variables that is also useful for simulating such random variables. Finally our results are applied to prove some inequalities concerning the total variation norm of the difference of two symmetric stable densities.},
author = {Kanter, Marek},
doi = {10.1214/aop/1176996309},
file = {:Users/samorris/Dropbox/Mendeley/The Annals of Probability/Kanter - 1975 - Stable Densities Under Change of Scale and Total Variation Inequalities.pdf:pdf},
issn = {0091-1798},
journal = {The Annals of Probability},
keywords = {monotone likelihood ratio,stable density,total variation distance,totally positive kernel,unimodal density},
month = aug,
number = {4},
pages = {697--707},
title = {{Stable Densities Under Change of Scale and Total Variation Inequalities}},
url = {http://projecteuclid.org/euclid.aop/1176996309},
volume = {3},
year = {1975}
}
@article{Jeon2012,
abstract = {The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial dependence structure in the extreme value analysis can be measured by max-stable processes. However, there have been few works on the threshold approach of max-stable processes. We propose a threshold version of max-stable process estimation and we apply the pairwise composite likelihood method by Padoan et al. (2010) to estimate spatial dependence parameters. It is of interest to establish limit behavior of the estimates based on the settings of increasing domain asymptotics with stochastic sampling design. Two different types of asymptotic normality are drawn under the second-order regular variation condition for the distribution satisfying the domain of attraction. The theoretical property of dependence parameter estimators in limiting sense is implemented by simulation and a choice of optimal threshold is discussed in this paper.},
archivePrefix = {arXiv},
arxivId = {1209.6344},
author = {Jeon, Soyoung and Smith, Richard L.},
eprint = {1209.6344},
file = {:Users/samorris/Dropbox/Mendeley/Extremes/Jeon, Smith - 2012 - Dependence Structure of Spatial Extremes Using Threshold Approach.pdf:pdf},
journal = {Extremes},
month = sep,
pages = {1--43},
title = {{Dependence Structure of Spatial Extremes Using Threshold Approach}},
url = {http://arxiv.org/abs/1209.6344},
year = {2012}
}
@book{Falk2011,
address = {Basel},
author = {Falk, Michael and H\"{u}sler, J\"{u}rg and Reiss, Rolf-Dieter},
doi = {10.1007/978-3-0348-0009-9},
file = {:Users/samorris/Dropbox/Mendeley/Unknown/Falk, H\"{u}sler, Reiss - 2011 - Laws of Small Numbers Extremes and Rare Events.pdf:pdf},
isbn = {978-3-0348-0008-2},
publisher = {Springer Basel},
title = {{Laws of Small Numbers: Extremes and Rare Events}},
url = {http://www.springerlink.com/index/10.1007/978-3-0348-0009-9},
year = {2011}
}
@article{Cooley2007,
author = {Cooley, Daniel and Nychka, Douglas and Naveau, Philippe},
doi = {10.1198/016214506000000780},
file = {:Users/samorris/Dropbox/Mendeley/Journal of the American Statistical Association/Cooley, Nychka, Naveau - 2007 - Bayesian Spatial Modeling of Extreme Precipitation Return Levels.pdf:pdf},
issn = {0162-1459},
journal = {Journal of the American Statistical Association},
keywords = {colorado,extreme value theory,generalized pareto distribution,hierarchical model,latent process},
month = sep,
number = {479},
pages = {824--840},
title = {{Bayesian Spatial Modeling of Extreme Precipitation Return Levels}},
url = {http://www.tandfonline.com/doi/abs/10.1198/016214506000000780},
volume = {102},
year = {2007}
}
@article{Cooley2012a,
abstract = {Phenomena such as air pollution levels are of greatest interest when observations are large, but standard prediction methods are not specifically designed for large observations. We propose a method, rooted in extreme value theory, which approximates the conditional distribution of an unobserved component of a random vector given large observed values. Specifically, for Z=(Z1,\ldots,Zd)T and Z−d=(Z1,\ldots,Zd−1)T, the method approximates the conditional distribution of [Zd|Z−d=z−d] when ∥z−d∥>r∗. The approach is based on the assumption that Z is a multivariate regularly varying random vector of dimension d. The conditional distribution approximation relies on knowledge of the angular measure of Z, which provides explicit structure for dependence in the distribution’s tail. As the method produces a predictive distribution rather than just a point predictor, one can answer any question posed about the quantity being predicted, and, in particular, one can assess how well the extreme behavior is represented. Using a fitted model for the angular measure, we apply our method to nitrogen dioxide measurements in metropolitan Washington DC. We obtain a predictive distribution for the air pollutant at a location given the air pollutant’s measurements at four nearby locations and given that the norm of the vector of the observed measurements is large.},
author = {Cooley, Daniel and Davis, Richard A. and Naveau, Philippe},
doi = {10.1214/12-AOAS554},
file = {:Users/samorris/Dropbox/Mendeley/The Annals of Applied Statistics/Cooley, Davis, Naveau - 2012 - Approximating the conditional density given large observed values via a multivariate extremes framework,.pdf:pdf},
issn = {1932-6157},
journal = {The Annals of Applied Statistics},
month = dec,
number = {4},
pages = {1406--1429},
title = {{Approximating the conditional density given large observed values via a multivariate extremes framework, with application to environmental data}},
url = {http://projecteuclid.org/euclid.aoas/1356629045},
volume = {6},
year = {2012}
}
@article{Cooley2012,
abstract = {We survey the current practice of analyzing spatial extreme data, which lies at the intersection of extreme value theory and geostatistics. Characterizations of multivariate max-stable distributions typically assume specific univariate marginal distributions, and their statistical applications generally require capturing the tail behavior of the margins and describing the tail dependence among the components. We review current methodology for spatial extremes analysis, discuss the extension of the finite-dimensional extremes framework to spatial processes, review spatial dependence metrics for extremes, survey current modeling practice for the task of modeling marginal distributions, and then examine max-stable process models and copula approaches for modeling residual spatial dependence after accounting for marginal effects.},
author = {Cooley, Daniel and Cisewski, Jessi and Erhardt, Robert J. and Mannshardt, Elizabeth and Omolo, Bernard Oguna and Sun, Ying},
file = {:Users/samorris/Dropbox/Mendeley/REVSTAT/Cooley et al. - 2012 - A survey of spatial extremes Measuring spatial dependence and modeling spatial effects.pdf:pdf},
journal = {REVSTAT},
keywords = {copula,extremal coefficient,hierarchical model,madogram,max-stable process,multivarate extreme value distribution},
number = {1},
pages = {135--165},
title = {{A survey of spatial extremes: Measuring spatial dependence and modeling spatial effects}},
url = {http://www.ine.pt/revstat/pdf/rs120106.pdf},
volume = {10},
year = {2012}
}
@article{Coles1999,
abstract = {Quantifying dependence is a central theme in probabilistic and statistical methods for multivariate extreme values. Two situations are possible: one where, in a limiting sense, the extremes are dependent; the other where, in the same sense, the extremes are independent. This paper comprises an overview of the principal issues through a unified approach which encompasses both these situations. Novel diagnostic measures for dependence are also developed which provide complementary information about different aspects of extremal dependence. The paper is written in an elementary style, with the methodology illustrated by application to theoretical examples and typical data-sets. These data-sets and the S-plus functions used for the analyses are available online.},
author = {Coles, Stuart and Heffernan, Janet and Tawn, Jonathan},
doi = {10.1023/A:31009963131610},
file = {:Users/samorris/Dropbox/Mendeley/Extremes/Coles, Heffernan, Tawn - 1999 - Dependence Measures for Extreme Value Analyses.pdf:pdf},
journal = {Extremes},
keywords = {asymptotic independence,bivariate extreme value distribution,copula,point processes},
number = {4},
pages = {339--365},
title = {{Dependence Measures for Extreme Value Analyses}},
url = {http://link.springer.com/article/10.1023/A:1009963131610},
volume = {2},
year = {1999}
}
@article{Chambers1976,
author = {Chambers, J. M. and Mallows, C. L. and Stuck, B. W.},
doi = {10.1080/01621459.1976.10480344},
file = {:Users/samorris/Dropbox/Mendeley/Journal of the American Statistical Association/Chambers, Mallows, Stuck - 1976 - A Method for Simulating Stable Random Variables.pdf:pdf},
issn = {0162-1459},
journal = {Journal of the American Statistical Association},
month = jun,
number = {354},
pages = {340--344},
title = {{A Method for Simulating Stable Random Variables}},
url = {http://www.tandfonline.com/doi/abs/10.1080/01621459.1976.10480344},
volume = {71},
year = {1976}
}
@article{Blanchet2010,
author = {Blanchet, J. and Lehning, M.},
doi = {10.5194/hess-14-2527-2010},
file = {:Users/samorris/Dropbox/Mendeley/Hydrology and Earth System Sciences/Blanchet, Lehning - 2010 - Mapping snow depth return levels smooth spatial modeling versus station interpolation.pdf:pdf},
isbn = {1425272010},
issn = {1607-7938},
journal = {Hydrology and Earth System Sciences},
month = dec,
number = {12},
pages = {2527--2544},
title = {{Mapping snow depth return levels: smooth spatial modeling versus station interpolation}},
url = {http://www.hydrol-earth-syst-sci.net/14/2527/2010/},
volume = {14},
year = {2010}
}
@article{Blanchet2011,
archivePrefix = {arXiv},
arxivId = {1111.7091v1},
author = {Blanchet, Juliette and Davison, Anthony C.},
doi = {10.1214/11-AOAS464},
eprint = {1111.7091v1},
file = {:Users/samorris/Dropbox/Mendeley/The Annals of Applied Statistics/Blanchet, Davison - 2011 - Spatial modeling of extreme snow depth.pdf:pdf},
issn = {1932-6157},
journal = {The Annals of Applied Statistics},
month = sep,
number = {3},
pages = {1699--1725},
title = {{Spatial modeling of extreme snow depth}},
url = {http://projecteuclid.org/euclid.aoas/1318514282},
volume = {5},
year = {2011}
}
